Lopez-Pamies and Idiart (2010, “Fiber-Reinforced Hyperelastic Solids: A Realizable Homogenization Constitutive Theory,” J. Eng. Math., 68(1), pp. 57–83) have recently put forward a homogenization theory with the capability to generate exact results not only for the macroscopic response and stability but also for the evolution of the microstructure in fiber-reinforced hyperelastic solids subjected to finite deformations. In this paper, we make use of this new theory to construct exact, closed-form solutions for the change in size, shape, and orientation undergone by the underlying fibers in a model class of fiber-reinforced hyperelastic solids along arbitrary 3D loading conditions. Making use of these results, we then establish connections between the evolution of the microstructure and the overall stress-strain relation and macroscopic stability in fiber-reinforced elastomers. In particular, we show that the rotation of the fibers may lead to the softening of the overall stiffness of fiber-reinforced elastomers under certain loading conditions. Furthermore, we show that this geometric mechanism is intimately related to the development of long-wavelength instabilities. These findings are discussed in light of comparisons with recent results for related material systems.